The most important thing to do to make something move smoothly is to have it follow an arc.
Almost everything in real life moves in arcs.

Once you've got it following a smooth arc, make sure the size of the shapes are consistent in each frame.

Spacing is very important. The further apart the drawings are, the faster it will move when played back.
A general guide in animation is 'slow-in, slow-out'. Which means you'd make drawings closer together at the start of a movement, then further apart in the middle of the movement, and then closer together once again when the movement is coming to a stop.

I've done a quick animation for you.
The Animator's Survival Kit is an essential book for animation if you're serious about it.

I agree with HK, plus would like to add that his blink was distracting for me because when the eye is shut, it is larger than when the eye is open. Can you make it more of a slit than tripling the size?